Structural Change in an Open Economy - canon-igs.org · Structural Change in an Open Economy Kei-Mu...

Introduction Model Model Mechanisms Dynamics Conclusion

Structural Change in an Open Economy

Kei-Mu YiFederal Reserve Bank of Minneapolis

Jing ZhangUniversity of Michigan

May 28, 20121

1The views expressed here are those of the authors are are not necessarily reflective of views of the Federal

Reserve Bank of Minneapolis or the Federal Reserve System.


Structural Change

Share of employment (16 advanced nations)

Sector 1870 1960 1987

Agriculture 0.49 0.17 0.06Services 0.24 0.44 0.63Manufacturing 0.27 0.39 0.30

Source: Maddison (1991)

Agriculture share declines over time.

Services share rises over time.

Manufacturing share first rises and then declines over time.


Global integration, Structural Change

World’s economies increasingly interlinked via trade.

In past 30-40 years many emerging market countries haveglobalized

Manufacturing labor shares are declining in developed nations,and rising (although not permanently) in emerging marketcountries.

Trade with emerging markets has been blamed for decliningmanufacturing employment in developed countries.

In most countries, manufacturing has the highest productivitygrowth.


U.S. and South Korea Manufacturing Employment Share

0

5

10

15

20

25

30

1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Perc

ent

Year

United States

South Korea

Labor Productivity Growth (1970-2005)

Country Agriculture Manufacturing Services

U.S. 1.5% 3.8% 0.7%South Korea 4.9% 7.0% 1.7%


South Korea’s Manufacturing Net Exports As Share of GDP


Manufacturing Trade and Employment

Figure: Manufacturing Net Exports and Manufacturing Employment

CANFINITAPRT

ESP

IDN

IND

JPN

KOR

PER PHL

THATWN

VEN

BOL

BRA

CHL

COL

CRIMEX

MYS

‐5%

0%

5%

10%

15%

20%

25%

ufacturing

Lab

or Sha

re, 1962‐2005

, Pe

rcen

tage Points

AUS

AUTBELCAN

DENFRAGER

ISLNLDNZL NOR

ESP

SWE

CHEGBR

USA ARG

‐25%

‐20%

‐15%

‐10%

‐15% ‐10% ‐5% 0% 5% 10% 15% 20% 25% 30%

Chan

ge in

Man

u

Change in Manufacturing Net Exports/GDP, 1962‐2005, Percentage Points


Services Employment and Trade

list = β0 + β1tradeit + β2gdppcit + γi + εit

i : country; t: period

list : services employment share

tradeit : exports+imports as a share of GDP

gdppcit : GDP per capita in 2005 international dollars

Table: Trade and Services Labor Share

tradeit gdppcit β0 R2 Obs

Fixed Effecta 0.0801 1.23e-5 0.369 0.67 379(0.0289) (1.12e-6) (0.0251)


Key Question

What is the effect of international trade on the process ofstructural change?


Our Approach

We develop a two-country, three-sector model with inter- andintra-sector Ricardian trade

We study the channels by which trade affects structuralchange:

Trade delinks sectoral production and sectoral expenditure:

Closed: labor share = expenditure share

Open: labor share = expenditure share + net export share

Trade allows countries to specialize, affecting net export shares

Trade changes relative prices, affecting expenditure shares

We demonstrate two ways in which open economy cangenerate hump pattern in manufacturing employment


Related Research

Models of structural change:

Closed-economy models: Kongsamut, Rebelo and Xie (2001)and Ngai and Pissarides (2007)

Open economy models:

Matsuyama (2009): an example with Ricardian framework

Coleman (2007): model in which large emerging marketcountry integrates with rest of world

Models of Ricardian trade: Eaton and Kortum (2002)


Two Groups of Theories of Structural Change

Non-homothetic preferences:

Engel (1895)

Kongsamut et. al (2001)

Sector-biased productivity growth:

Baumol (1967)

Ngai and Pissarides (2007)

Closed economy frameworks


Model Set Up

Two countries

Three sectors: agriculture, manufacturing, services

Agriculture and manufactured goods are tradable

Services are nontradable

One factor: labor with exogenous supply

Mobile across sectors, but immobile across countries

Productivity growth differs across sectors and countries

Free trade: based on Ricardian comparative advantage


Technologies

Services: a single good Yist = AistList

Agriculture and manufacturing: a continuum of goods

yimt(z) = Aimt(z)Limt(z) z ∈ [0, 1]

yiat(z) = Aiat(z)Liat(z) z ∈ [0, 1]

A is distributed as Frechet: Fiqt(z) = exp(−Tiqtz−θ)

Goods are combined to yield composite goods for consumption


Prices

Perfect competition in goods and factor markets

Service good price: Pist = witAist

Agricultural good price:

piat(z) = min

{w1t

A1at(z),

w2t

A2at(z)

}Manufacturing good price:

pimt(z) = min

{w1t

A1mt(z),

w2t

A2mt(z)

}


Preferences

Tradable sector composite goods: elasticity of substitution η

Ciqt = (∫ 1

0 ciqt(z)η−1η dz)

ηη−1

Intratemporal utility: elasticity of substitution ε

Cit = (ωaCε−1ε

iat + ωmCε−1ε

imt + ωsCε−1ε

ist )εε−1

Intertemporal utility:∑∞

t=0βtU(Cit)

Budget constraint (period-by-period):

PitCit = PiatCiat + PimtCimt + PistCist = witLit


Expenditure Shares

Expenditure share:

Xiqt =PiqtCiqt

witLit= ωεq

(Piqt

Pit

)1−ε

Aggregate price:

Pit =(ωεaP

1−εiat + ωεmP

1−εimt + ωεsP

1−εist

) 11−ε

Sectoral composite good price:

Piqt =

(∫ 1

0

piqt(z)η

η−1 dz

) η−1η


Market Clearing Conditions

Labor markets:

Lit = List +∫ 1

0 Limt(z)dz +∫ 1

0 Liat(z)dz , i = {1, 2}

Services good markets:

Yist = Cist , i = {1, 2}

Agriculture goods markets:∑2i=1 yiat(z) =

∑2i=1 ciat(z) ∀z ∈ [0, 1]

Manufacturing goods markets:∑2i=1 yimt(z) =

∑2i=1 cimt(z) ∀z ∈ [0, 1]


Open-Economy Equilibrium

A competitive equilibrium is a sequence of goods and factor prices{piat(z), pimt(z), Piat , Pimt , Pist , Pit , wit}∞t=0 and allocations{liat(z), limt(z), Liat , Limt , List , yiat(z), yimt(z), Yist , ciat(z),cimt(z), Ciat , Cimt , Cist , Cit}∞t=0 for z ∈ [0, 1] and i = 1, 2, suchthat given prices, the allocations solve the firms’ maximizationproblems and the household’s maximization problem, and satisfythe market clearing conditions.


Closed Economy Equilibrium

Sectoral labor share = sectoral expenditure share

lqt =LqtLt

=wtLqtwtLt

=PqtCqt

PtCt= Xqt

Expenditure share:

Xqt = ωεq

(Pqt

Pt

)1−ε

Prices: Pqt = wtAqt

, where Aqt = T1/θqt /γ.


Closed Economy Dynamics

Lqt = Xqt = (1− ε)(Pqt − (Xat Pat + Xmt Pmt + Xst Pst)

)

= (ε− 1)(Aqt − (XatAat + XmtAmt + XstAst)

)

ε = 1: no structural change

ε < 1: labor moves from the highest productivity growthsector to the lowest productivity growth sector

ε > 1: labor moves from the lowest productuviity growthsector to the highest productivity growth sector


Key Implications of Closed Economy

Preferences play a major role in labor allocation across sectors.

Structural change does not occur if the elasticity ofsubstitution equals one.

With elasticity of substitution less than one:

The high productivity growth sectors experience decliningrelative prices, expenditure shares and labor shares.

Labor moves from the most productive sector to the leastproductive sector.


Key Ingredients of Open Economy

Trade based on comparative advantage (Ricardian)

Assume country 1 has a comparative advantage inmanufacturing.

That is, under free trade,

A1mt

A2mt>

A1at

A2at.

Under free trade, the LOOP holds: p1qt(z) = p2qt(z).

Tradable composite good prices are equalized acrosscountries: P1qt = P2qt .


Open Economy: Prices

Under Frechet distribution (and free trade):

Piqt =

[(witAiqt

)−θ+(

wjt

Ajqt

)−θ]− 1θ

Piqt

wit= 1

Aiqt

[1 +

(wjt

wit

Aiqt

Ajqt

)−θ]− 1θ

Services price: Pistwit

= 1Aist


Prices in Open vs. Closed Economy

Piatwit

and Pimtwit

are lower in open economy

Pistwit

is the same

Pitwit

is lower in open economy

Welfare is higher in open economy

PistPit

rises, P1atP1t

and P2mtP2t

declines in open economy

P1mtP1at

is higher in the open economy


Expenditure Shares in Open vs. Closed Economy

Relative prices and the elasticity of substitution play key rolein determining expenditure shares Xiqt .

With elasticity less than one, in both countries in openeconomy,

services expenditure shares are higher;

expenditure share of the sector with comparative disadvantageis lower;

expenditure share of the sector with comparative advantage isambiguous.


Open Economy: Intra-Sector Trade

In addition to (sectoral) expenditure shares, another share matters:the share of sectoral spending that is on imports:

Share of country 1’s expenditure on sector q goods fromcountry 2 (under free trade):

π12qt =(w2t/A2qt)

−θ

(w2t/A2qt)−θ + (w1t/A1qt)−θ=

1

1 + (w1t/A1qt

w2t/A2qt)−θ

π12qt rises as w2t/A2qt decreases relative to w1t/A1qt

The rise is larger with larger θ (a low productivity dispersion)

Comparative advantage implies π12mt < π12at


Open Economy: Inter-Sector Trade

Putting together these two shares:

Manufacturing net exports of country 1 as share of its GDP:

N1mt =π21mtX2mtw2tL2t

w1tL1t− π12mtX1mt

Comparative advantage implies N1mt > 0 and N1at < 0.

The net export ratio of the sector with comparative advantage ispositive in each country.


Open Economy: Labor Allocation

Services labor share: list = List/Lit = Xist

Manufacturing labor share of country i:

limt =Limt

Lit= Ximt + Nimt

Direct contribution of trade: Nimt

Country 1 has a comparative advantage in manufacturing

N1mt > 0 and N2mt < 0

Indirect contribution of trade: Ximt

Similarly for agriculture labor share


Labor Dynamics

Growth in manufacturing labor share:

l1mt =X1mt

l1mtX1mt +

N1mt

l1mtN1mt

First term: the expenditure effect

Second term: the trade or net export effect

Positive growth in manufacturing net export share contributespositively to labor share.

To focus on trade effect, consider case with elasticity ofsubstitution across sectors = 1; hence, X1mt = 0


Impact of Trade on Structural Change


Productivity Growth and Hump Pattern in Manufacturing

Necessary condition for N1mt > 0: Amt > Aat , (Aqt =A1qt

A2qt)

Under free trade, manufacturing labor share equation:

l1mt = ωmπ11m

(wtL1t + L2t

wtL1t

)π11m = π21m: specialization term

Reciprocal of GDP share: country-size term

As manufacturing productivity grows, specialization termcontributes positively to manufacturing labor share, whilecountry-size term contributes negatively.

Each country buys more of its manufactured goods fromcountry 1 (e.g., South Korea).

If Aat > 0, country 1 relative wage grows, country 2 (e.g.,United States) purchasing power falls. Country 1 needs lesslabor to meet country 2 demand.


Productivity Growth and Hump Pattern in Manufacturing

Initially, specialization term is dominant.

Eventually, country-size term dominates.

Once manufacturing becomes close to completely specialized,employment growth from specialization effect becomes small.

In limiting case, country 2 buys all its manufactured goodsfrom country 1, but country 2 has zero mass, so the globaleconomy is effectively just country 1.

Country 1 employment share declines until it equalsexpenditure share.


Structural Change in Open Economy: Example 1

Preferencesε = 0.5 σ∗ = 1.0ωa = 1/3 ωm = 1/3 ωs = 1/3

Labor Endowment

L10 = 1 L20 = 10 L1t = L1t = 1.0

Sectoral Productivitiesθ = 4.0A1a0 = 1.0 A1m0 = 1.0 A1s0 = 1.0

A2a0 = A1a0(L20/L10)1/θ A2m0 = A1m0(L20/L10)1/θ A2s0 = A1s0(L20/L10)1/θ

A1at = 1.01 A1mt = 1.02 A1st = 1.0

A2at = 1.02 A2mt = 1.01 A2st = 1.0


Structural Change in Country 1

Figure: Employment Shares, Closed and Open

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Exp & labor share, closedExp share, openLabor share, open

(a) Agriculture

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(b) Manufacturing

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(c) Services




0 20 40 60 80 1000.1

0.2

0.3

0.4

0.5

Exp & labor share, closedExp share, openLabor share, open

(a) Agriculture

0 20 40 60 80 1000.1

0.2

0.3

0.4

0.5

(b) Manufacturing

0 20 40 60 80 1000.1

0.2

0.3

0.4

0.5

(c) Services


Import Shares

Figure: Import Shares

0 20 40 60 80 1000.7

0.8

0.9

1

1.1

AgricultureManufacturing

(a) Country 1

0 20 40 60 80 1000

0.05

0.1

0.15

0.2

0.25

(b) Country 2


Wages, Prices, and Welfare

Figure: Wages, Prices, and Welfare

0 20 40 60 80 1000.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1 Open2 Open

(a) Wages

0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3

1 Open2 Open1&2 Closed

(b) Prices

0 20 40 60 80 1000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 Open2 Open1 Closed2 Closed

(c) Welfare


Structural Change and Trade Costs

Introduce iceberg trade costs

Prices:

Piqt =[(wit/Aiqt)

−θ + (τqtwjt/Ajqt)−θ]− 1

θ

Import shares:

πijqt =(τqtwjt/Ajqt)

−θ

(τqtwjt/Ajqt)−θ + (wit/Aiqt)−θ.

Decline in τqt affects Piqt and πijqt like increase in Ajqt

Decline in trade costs can also generate structural change,even in absence of biased sectoral productivity growth


Trade Costs and Hump Pattern in Manufacturing

Suppose country 1 has comparative advantage inmanufacturing and is small relative to country 2.

Productivity levels are constant over time

As trade costs decline, specialization increases (manufacturingnet export surplus grows) and country 1 relative wage rises

Initially, specialization effect dominates country-size effect, somanufacturing labor share in country 1 rises

Eventually, country 1 labor used to satisfy country 2manufacturing demand declines, so manufacturing labor sharein country 1 falls


Structural Change in Open Economy: Example 2

Preferencesε = 0.5 σ∗ = 1.0ωa = 1/3 ωm = 1/3 ωs = 1/3

Labor Endowment

L10 = 1 L20 = 10 L1t = L1t = 1.0

Sectoral Productivitiesθ = 4.0A1a0 = 1.5 A1m0 = 2.0 A1s0 = 1.0

A2a0 = 2.0(L20/L10)1/θ A2m0 = 1.5(L20/L10)1/θ A2s0 = 1.0(L20/L10)1/θ

A1at = 1.0 A1mt = 1.0 A1st = 1.0

A2at = 1.0 A2mt = 1.0 A2st = 1.0

Trade Costsτq0 = 2.5 τqt − 1 declines at 3% per period




0 10 20 30 400

0.1

0.2

0.3

0.4

Exp & labor share, closedExp share, open Labor share, open

(a) Agriculture

10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

(b) Manufacturing

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

(c) Services


Conclusion

International trade provides environment in which sectoraloutput and sectoral expenditure need not be equal

With neoclassical trade, comparative advantage interacts withglobal sectoral demand to determine patterns of expenditure,trade, production, and employment

We study structural change in an open economy with modelthat highlights these themes

Model yields rich insights and can potentially better explainpatterns in data

Extending model to include non-homothetic preferences,intermediate goods, and trade costs does not alter the mainimplications

Companion project: quantitative assessment


Accounting: the U.S.

Year lmt Xmt Nmt Xmt + Nmt

1970 25.6% 27.9% -1.1% 26.8%

2000 14.5% 21.6% -4.8% 16.8%

Change -11.1% -6.3% -3.7% -10.0%

The direct trade effect accounts for one third of the decline inUS manufacturing labor share.


Accounting: the U.K.

Year lmt Xmt Nmt Xmt + Nmt

1970 34.6% 31.0% 2.4% 33.4%

2000 16.8% 22.9% -7.8% 15.1%

Change -17.8% -8.1% -10.2% -18.3%

The direct trade effect accounts for more than one half of thedecline in British manufacturing labor share.


Manufacturing Labor Share and Income

0

5

10

15

20

25

30

35

40

0 5000 10000 15000 20000 25000 30000 35000 40000

US Korea UK Japan

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